Measurement of the Transverse Beam Spin Asymmetry in Elastic Electron-Proton Scattering and the Inelastic Contribution to the Imaginary Part of the Two-Photon Exchange Amplitude

We report on a measurement of the asymmetry in the scattering of transversely polarized electrons off unpolarized protons, $A_{\perp }$, at two $Q^2$ values of 0.106 and $0.230(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^2$ and a scattering angle of $30°<{\theta }_e<40°$. The measured transverse asymmetries are $A_{\perp }\mathbf{(}{Q}^2=0.106(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^2\mathbf{)}=(-8.59\pm {0.89}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.75}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\times {10}^{-6}$ and $A_{\perp }\mathbf{(}{Q}^2=0.230(\mathrm{G}\mathrm{e}\mathrm{V}/c{)}^2\mathbf{)}=(-8.52\pm {2.31}_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}\pm {0.87}_{\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}})\times {10}^{-6}$. The first errors denote the statistical error and the second the systematic uncertainties. From comparison with theoretical estimates of $A_{\perp }$ we conclude that $\pi N$-intermediate states give a substantial contribution to the imaginary part of the two-photon amplitude. There is no obvious reason why this should be different for the real part of the two-photon amplitude, which enters into the radiative corrections for the Rosenbluth separation measurements of the electric form factor of the proton.